CN104484723A - Power transformer economic life prediction method based on life data - Google Patents
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Abstract
Currently, a unified definition for the economic life of transformers is not formed at home and abroad, and the study mainly focuses on economic evaluation. The invention provides a power transformer economic life prediction method based on life data. According to the method, a transformer economic life prediction model with the EUAC (equivalent uniform annual cost) minimum taken as a basis is constructed, classification and critical data extraction are performed on full-life data of a transformer for calculation of critical parameters in the model, and the failure rate and probability distribution of the shutdown duration are acquired through calculation with a distribution-free PHM (proportional hazards model) and a Monte Carlo simulation method; then economic elements are analyzed, and quantitative prediction about the economic life of the power transformer is realized on the basis of calculation of the annual maintenance cost, the annual interruption cost and the annual operation cost of the power transformer. With the adoption of the method, the life data of equipment can be effectively utilized, a prediction result is reasonable, and the method has the guiding significance to operation and maintenance decisions as well as planning and transformation of future transformer substations.
Description
Technical field
The invention belongs to field of power, specifically a kind of power transformer Forecast of Economic Life method based on lifetime data.
Background technology
Assets whole-life cycle fee is the research field that power grid enterprises very pay attention to.If by the future life of known lifetime data predict device, be then not only of value to the selection of equipment O&M strategy, Electric Power Network Planning can also be instructed.As equipment most important in transformer station, the quantitative forecast of service life of power transformer can provide important evidence for the life prediction of transformer station, contributes to extending transformer station's active time, improves security and the economy of operation of power networks.
The life-span of power transformer is divided into physical life, technical life and economic life usually.The Main Basis of physical life prediction is insulation ag(e)ing degree, needs the insulating property information of measuring transformer inside, and as the tensile strength etc. of the degree of polymerization, furfural number and insulating paper, this kind of data are often difficult to obtain, therefore physical life prediction comparatively difficulty.Technical life is often referred to the designed life of transformer, generally rule of thumb artificially specifies.Economic life is the survival condition information (as hydrocarbon information etc.) based on transformer, determines the transformer retired time from economics point.Therefore, the research of power transformer Forecast of Economic Life has more feasibility and practical significance.Do not form the unified definition of transformer economic life at present both at home and abroad, research mainly concentrates in economic evaluation.
Along with the development of status monitoring and assessment technology, and the attention of power grid enterprises' Assets Management, the economic life research that increases to of transformer life data provides good Information base.
Summary of the invention
Technical matters to be solved by this invention is the defect overcoming the existence of above-mentioned prior art, a kind of power transformer Forecast of Economic Life method based on lifetime data is provided, it takes into full account the existing lifetime data of power transformer, utilize historical data as much as possible, to improve confidence level and the rationality of result.
For this reason, the present invention adopts following technical scheme: a kind of power transformer Forecast of Economic Life based on lifetime data, is characterized in that,
First, minimum as retired foundation with transformer year equivalent cost (EUAC, equivalent uniform annual cost), propose the economic life model of power transformer;
Then, classify and extract lifetime data, the proportional hazards model of selection distribution-free and Monte Carlo Analogue Method calculate the key parameter in the failure rate of power transformer and these two models of probability distribution of downtime duration;
Finally, integrated economics key element, proposes the computing method of the annual overhaul cost of transformer, outage cost, operating cost and present worth, realizes solving of Forecast of Economic Life model, obtain the optimal economic life-span of power transformer based on lifetime data.
The present invention has taken into full account the existing lifetime data of power transformer, in conjunction with historical data, makes result of calculation have more confidence level.The power transformer economic life utilizing the present invention to judge, the selection of the following O&M strategy of power transformer can not only be instructed, also can instruct the future plan of affiliated transformer station.In addition, can also the present invention be used for reference, according to life information and the feature of other type equipment, set up the Forecast of Economic Life method of other type of electrical power equipment.
The present invention adopts following concrete steps:
Step 1), the foundation of the economic life model of power transformer;
According to cash flow diagram, past value in different time points or future value need conversion to reference time value, the present worth of certain moment amount of money is represented with P, F represents the final value of equivalence of a certain moment amount of money in the future, A represent fund on schedule single-candidate pay annuity, i.e. year equivalent cost EUAC, the conversion relation between them is as follows:
F＝P(1+i)
n，
In various above, i is discount rate; N is the conversion time limit;
During M+m, the total cost final value of transformer is:
In formula, M is the current enlistment age, and m is the m that will predict from the current enlistment age; FV
m+mthe cost final value of indication transformer M+m; C is transformer cost of capital; PV (M+m) is the present worth of transformer M+m after depreciation; C
aj () is the annual total cost in transformer jth year, wherein, the annual total cost now before M in age adopts historical data, and the data after existing age are predicted value;
EUAC is converted into by total cost final value:
In formula, EUAC
m+meUAC value during indication transformer M+m;
The cost of capital of power transformer is comparatively large, mid-term first in operation, and failure rate is low, its annual total cost is lower, and therefore EUAC reduces year by year usually.When the operation later stage, transformer survival condition is deteriorated, and annual total cost raises, and EUAC will rise year by year.If the EUAC predicted value that power transformer showed after age does not have minimum point, year, cost was in continuous rising, should consider to change as early as possible; If EUAC predicted value has minimum point, enlistment age corresponding to this minimum point be year cost minimum, now retired is the optimal economic life-span.
Step 2), the classification of life-cycle data and extraction;
The develop and practice of transformer whole-life cycle fee and Condition-Based Maintenance Technology have accumulated numerous lifetime data, for the calculating of model parameter provides condition.By analysis, transformer life-cycle data are divided into six classes, be respectively: basic data (electric pressure, capacity, manufacturer, the date of production, put into operation the date, designed life, the main technical characteristics data such as open circuit loss), inspect data and (patrol and examine data, test figure, maintenance defect elimination record, live detection data etc.), real time data (operating condition data, on-line condition monitoring data, information about power data etc.), environmental data (temperature, humidity, air pressure, filthy, the outside weather environmental impact data etc. such as thunder and lightning), economic data (equipment cost of capital, infrastructure project expense, maintenance human cost, interest rate, trucking costs, outage cost, the monthly unit electricity charge) and other data (comprising the information data etc. of standby redundancy).Continue every class data analysis, select significant data to be used for the calculating of Parameters in Mathematical Model.
Step 3), model parameter calculation;
From step 1), calculate EUAC and predict that the method for economic life is relevant with present worth with the annual total cost of power transformer, wherein: present worth is calculated by the depreciation method; Annual total cost needs the cost of overhaul and annual outage cost computation year, and relate to the calculating of transformer reliability index and downtime duration probability distribution, the calculating of these two parameters is comparatively crucial.
(1) foundation of failure rate forecast model
Use for reference widely used theory of survival analysis in medical science, the covariant set up the condition failure rate function on affecting survival condition: proportional hazards model (Proportional Hazards Model, PHM).This model is regression model, and its mathematic(al) representation is as follows:
λ(t|Z)＝λ
0(t)c(β
TZ)
In formula: λ
0t () is benchmark failure rate, relevant to the enlistment age, can represent, as Weibull distribution etc., also can represent with arbitrary distribution-free nonnegative function with specifically determining distribution parameter form; Z=(z
1, z
2..., z
p)
tfor covariant vector, covariant is the state variable of reflection equipment health condition, and p is covariant number, and T represents the transposition of vector; β=(β
1, β
2..., β
p)
tfor unknown regression coefficient vector; Contiguous function c is any nonnegative function, the simple exponential function of normal different forms, and namely the expression formula of PHM is as follows:
λ(t|Z)＝λ
0(t)exp(β
TZ)，
Set up the proportional hazards model of power transformer, key will select and set up covariant.The lifetime data relevant with failure rate is also more, for obtaining fewer but better covariant, and ensures independence and the representativeness of covariant, to above-mentioned data acquisition logic inductive method, condensed go out 7 covariants, be respectively: outward appearance (z
1), machinery (z
2), insulation (z
3), enlistment age (z
4), geographical running environment (z
5), capacity-load ratio (z
6) and manufacturer (z
7).Outward appearance, machinery and insulation are the classification of health indicator (HI, Health Index), have reacted the holistic health level of transformer equipment self, are the various combined reactions inspecting data and real time data.If transformer has recent state evaluation result, then can directly use; Otherwise carry out concentrated expression by outward appearance, machinery, insulation three covariants.Outward appearance reflection leakage of oil, oil impregnate, surface corrosion etc., machinery reflection refrigeratory, fan ruuning situation etc., insulation main reflection dissolved gas analysis result.During application, there are five grades in HI and subordinate's covariant: normal, note, serious, urgent and fault.For ease of quantitative comparison, specify above-mentioned covariant according to the form below value.
The equipment enlistment age after operation the impact of phase on survival condition be generally acknowledged, therefore as a covariant, its unit is year, round numbers.Geographical running environment is as the covariant of concentrated expression environmental data, reason is that other environmental data constantly changed in 1 year, and be much the same for areal distinct device, therefore select plot character belonging to running environment more can reflect the living environment of transformer.Manufacturer is selected to be because different manufacturers may exist familial defect as covariant.The survival condition impact of information about power on transformer is obvious, and electricity factor comprises voltage, electric current, load factor and capacity-load ratio etc., and the present invention selects capacity-load ratio conventional in Electric Power Network Planning as a covariant, and unit is kVA/kW.Above-mentioned covariant, in commission transformer, geographical running environment and manufacturer are fixing and non-time-varying.
The above-mentioned 7 kinds of covariants of power transformer are all relevant to equipment survival condition, are labeled as z
1(t) ~ z
7t (), if z
kt () (k=1 ~ 7) had nothing to do with the time, be then expressed as z
k.For i-th transformer, its ratio failure rate function is as follows:
λ
i(t|Z
i(t))＝λ
0(t)exp(β
i TZ
i(t))
＝λ
0(t)exp(β
1z
i1(t)+β
2z
i2(t)+
…+β
7z
i7(t))
In formula: time t and covariant vector Z are known quantity; λ
0t () and regression coefficient vector β are unknown quantity.Work as λ
0when () is half parameter of distribution-free t, " partial likelihood function " method can be adopted to solve regression coefficient β.
(2) Monte Carlo Analogue Method determines the probability distribution of break period
Monte Carlo Analogue Method has good dirigibility and practicality.The present invention adopts sequential Monte Carlo simulation to set up the probability distribution of downtime duration, and utilization state duration sampling sets up virtual state transfer cycle process.Power transformer only has two states usually: run and stop transport.Stop transport and be divided into two states again: by forced-stopping machine (breaking down) and scheduled overhaul.Carry out state duration sampling,
A) original state is specified.Suppose that all transformers are all in running status, running status is 1, and shut down condition is 0, simultaneously number n of given emulation total year;
B) duration of each transformer current state is sampled, and the probability distribution of set condition duration (exponential distribution or lognormal distribution);
C) in studied time span, step b is repeated), namely obtain the time sequence status transfer process of a certain transformer in institute's search time span and combine, until terminate emulation when simulation time is greater than or coefficient of variation is less than the condition of convergence.A certain transformer combines is existed four kinds of states by after forced-stopping machine and scheduled overhaul, is respectively 11 (normally running), 10 (scheduled maintenances), 01 (breakdown maintenance) and 00 (time of carrying out breakdown maintenance was just in time in the time of original scheme of arrangement maintenance).Except 11 states, its excess-three kind state all belongs to " shutdown ".
Solve four state sequence Monte Carlo simulations, the probability distribution of downtime duration can be obtained.
Step 4), transformer Forecast of Economic Life model solution
According to step 1), calculate EUAC and predict that the method for economic life is relevant with the annual total cost CA of power transformer, annual total cost is calculated as follows:
C
A(t)＝C
R(t)+C
I(t)+C
O(t)
In formula, C
rt () is the annual overhaul cost of t; C
it () is the annual outage cost of t; C
ot () is the annual operating cost of t.
Meanwhile, the calculating of EUAC is also relevant with the present worth of power transformer, and computing method are as follows:
In formula, PV (t) is the transformer present worth in the t end of the year;
be the accumulated depreciation expense to t from First Year, other variable is with the formula in step 1).
The calculating of amortization charge needs the choice and operation considering depreciation method.The conventional time-based depreciation method is straight-line depreciation and accelerated depreciation.Straight-line depreciation and depreciation composite life, refer to a kind of method by the average calculating and distilling depreciation tenure of use of capital assets, discount rate is fixed; Accelerated depreciation method is divided into double decling balance method and sum of the years digits method.Wherein sum of the years digits method, the method that the year number mark referring to the state of tapering off distributes cost.Because power transformer is along with the increase of tenure of use, failure rate can rise, especially after operation the phase, and the value of transformer is substantially equal to residual value.Therefore, when transformer tenure of use more than 20 years time the present invention select sum of the years digits method computing depreciation expense, then adopted straightline method of depreciation before 20 years.
Further, step 4) in, being calculated as follows of annual each cost:
(1) annual overhaul cost C
r
C
R(t)＝(a×r
a+b)×λ(t)
In formula, C
rt () is the annual overhaul cost of t; A is for shutting down variable maintenance cost hourly; B is each fixing maintenance cost of interrupting; r
abe the mean down time of each fault of t, by step 3) in Monte Carlo Analogue Method try to achieve; λ (t) is the failure rate of transformer t, by step 3) in proportional hazards model try to achieve.The cost unit related in formula is " unit ", and the value of a and b is determined according to transformer running environment and regional economy situation.
(2) annual outage cost C
i
Transformer stoppage in transit can have influence on power supply reliability, causes the loss of user.Can simplify and think that this part loss is for outage cost expense, need to select to set up the outage cost function relevant with downtime duration for this reason.Unit outage cost and downtime duration have with customer type relevant, determine according to the powered types in the geographical environment of power transformer place.The unit outage cost function of different downtime duration, in conjunction with probability distribution stop time that Monte Carlo Analogue Method obtains, can predict the outage cost expense under specific load (kW) when obtaining each fault.Therefore annual outage cost formula is as follows:
In formula: C
it () is the outage cost of t, be the mean value of probability distribution; λ (t) is the failure rate of t; L
avfor the average load of transformer; SCDF
tit is the outage cost expense of t specific load (kW); K is downtime duration, by hour in units of, assuming that scope is [0,70]; p
ktto be t downtime duration the be probability of k hour, by step 3) in Monte Carlo Analogue Method try to achieve; C
tkfor the unit outage cost expense that downtime duration is k hour.
(3) annual operating cost C
o
Annual operating cost is made up of two parts: energy loss cost and demand cost.Energy loss cost is relevant with the energy tax rate, because China does not set up special energy tax item, the tax category such as value added tax, the consumption tax all may with energy loss costs associated, weigh very difficult, therefore the present invention does not consider energy loss cost.Therefore, annual operating cost is exactly demand cost, as shown in the formula:
C
O(t)＝(P
nl+P
l+P
au)×D
c×12
In formula: C
ot () is the operating cost of t; P
nlfor no-load power loss (kW); P
lfor load loss (kW); P
aufor added losses (kW); D
cfor the demand electricity charge (unit/kW) monthly.
Present invention incorporates the lifetime data of power transformer, compared with the power transmission and transforming equipment bathtub curve matching forecast model of single enlistment age variable or single state variable in the past, Power Transformer Faults rate is predicted the outcome more reasonable.Predict the outcome and can not only instruct the selection of the following O&M strategy of power transformer, also can instruct the future plan of affiliated transformer station.
Accompanying drawing explanation
Fig. 1 is equipment cash flow diagram;
Fig. 2 is EUAC curvilinear trend figure;
Fig. 3 is transformer Forecast of Economic Life foundation and process;
Fig. 4 is transformer survival condition covariant;
Fig. 5 (a) ~ (c) is transformer time sequence status sampling schematic diagram;
Fig. 6 is the unit outage cost expense of different downtime duration;
Fig. 7 a is the annual each cost volume example of active service transformer in application examples; Fig. 7 b is the probability distribution that in application examples, stop time predicted on the 23rd year by active service transformer; Fig. 7 c is the present worth of active service power transformer in application examples; Fig. 7 d is the EUAC value of application examples active service transformer.
Embodiment
Below in conjunction with Figure of description, the invention will be further described, the present invention includes following steps:
Step (1), the foundation of the economic life model of power transformer.Specifically:
According to Fig. 1, the past value in different time points or future value need conversion to reference time value.
During M+m, the total cost final value of transformer is:
In formula: M is the current enlistment age, m is the m that will predict from the current enlistment age; FV
m+mthe cost final value of indication transformer M+m; C is transformer cost of capital; PV (M+m) is the present worth of transformer M+m after depreciation; C
aj () is the annual total cost in transformer jth year, wherein, the annual total cost now before M in age can adopt historical data, and the data after existing age are predicted value.
Can EUAC be converted into by total cost final value:
In formula, EUAC
m+meUAC value during indication transformer M+m.
Have two kinds to move towards trend according to Fig. 2, EUAC curve, curve tendency one means that the EUAC predicted value that power transformer showed after age does not have minimum point, and year, cost was in continuous rising, should consider to change as early as possible; Curve tendency two means that EUAC predicted value has minimum point, enlistment age N corresponding to this minimum point be year cost minimum, now retired is the optimal economic life-span.
Step (2), the classification of life-cycle data and extraction.Specifically:
Calculate EUAC and predict that the method for economic life is relevant with present worth with the annual total cost of power transformer.Wherein: present worth is calculated by the depreciation method; Annual total cost needs the cost of overhaul and annual outage cost computation year, and relate to the calculating of transformer reliability index and downtime duration probability distribution, the calculating of these two parameters is comparatively difficult, needs the lifetime data of dependence equipment.The develop and practice of transformer whole-life cycle fee and Condition-Based Maintenance Technology have accumulated numerous lifetime data, for the calculating of model parameter provides condition.By analysis, transformer life-cycle data are divided into six classes, as shown in table 1.
Table 1 power transformer life-cycle Data classification
Continue every class data analysis, select significant data to be used for the calculating of correlation parameter.After transformer life-cycle Various types of data is extracted, establish Forecast of Economic Life foundation as shown in Figure 3 and process schematic.Significant data in life-cycle, for key parameter and year each cost calculating.
Step (3), the calculating of model parameter.Specifically:
(1) foundation of failure rate forecast model
Use for reference widely used theory of survival analysis in medical science, the covariant set up the condition failure rate function on affecting survival condition: proportional hazards model (Proportional Hazards Model, PHM).This model is regression model, and its mathematic(al) representation is as follows:
λ(t|Z)＝λ
0(t)c(β
TZ)
In formula: λ
0t () is benchmark failure rate, relevant to the enlistment age, can represent, as Weibull distribution etc., also can represent with arbitrary distribution-free nonnegative function with specifically determining distribution parameter form; Z=(z
1, z
2..., z
p)
tfor covariant vector, covariant is the state variable of reflection equipment health condition, and p is covariant number, and T represents the transposition of vector; β=(β
1, β
2..., β
p)
tfor unknown regression coefficient vector; Contiguous function c is any nonnegative function, the simple exponential function of normal different forms, and namely the expression formula of PHM is as follows:
λ(t|Z)＝λ
0(t)exp(β
TZ)
Set up the proportional hazards model of power transformer, key will select and set up covariant.The lifetime data relevant with failure rate is also more, for obtaining fewer but better covariant, and ensures independence and the representativeness of covariant, to above-mentioned data acquisition logic inductive method, condensed go out 7 covariants, as Fig. 4.
Health indicator (HI, Health Index) reflects the holistic health level of transformer equipment self, is the various combined reactions inspecting data and real time data.If transformer has recent state evaluation result, then can directly use; Otherwise carry out concentrated expression by outward appearance, machinery, insulation three covariants.Three covariants are concluded with reference to directive/guide document, outward appearance reflection leakage of oil, oil impregnate, surface corrosion etc., machinery reflection refrigeratory, fan ruuning situation etc., insulation main reflection dissolved gas analysis result.During application, there are five grades in HI and subordinate's covariant: normal, note, serious, urgent and fault.For ease of quantitative comparison, specify above-mentioned covariant according to the form below 2 value.
Table 2 HI state variable calculates value
The equipment enlistment age after operation the impact of phase on survival condition be generally acknowledged, therefore as a covariant, its unit is year, round numbers.Geographical running environment is as the covariant of concentrated expression environmental data, reason is that other environmental data constantly changed in 1 year, and be much the same for areal distinct device, therefore select plot character belonging to running environment more can reflect the living environment of transformer.Manufacturer is selected to be because different manufacturers may exist familial defect as covariant.The survival condition impact of information about power on transformer is obvious, and electricity factor comprises voltage, electric current, load factor and capacity-load ratio etc., and the present invention selects capacity-load ratio conventional in Electric Power Network Planning as a covariant, and unit is kVA/kW.For in commission transformer, geographical running environment and manufacturer are fixing and non-time-varying.
These 7 kinds of covariants of power transformer are all relevant to equipment survival condition, are labeled as z
1(t) ~ z
7t (), if z
kt () (k=1 ~ 7) had nothing to do with the time, be then expressed as z
k.For i-th transformer, its ratio failure rate function is as follows:
λ
i(t|Z
i(t))＝λ
0(t)exp(β
i TZ
i(t))
＝λ
0(t)exp(β
1z
i1(t)+β
2z
i2(t)+
…+β
7z
i7(t))
In formula: time t and covariant vector Z are known quantity; λ
0t () and regression coefficient vector β are unknown quantity.Work as λ
0when () is half parameter of distribution-free t, " partial likelihood function " method can be adopted to solve regression coefficient β.
(2) Monte Carlo Analogue Method determines the probability distribution of break period
Monte Carlo Analogue Method has good dirigibility and practicality.The present invention adopts sequential Monte Carlo simulation to set up the probability distribution of downtime duration, and utilization state duration sampling sets up virtual state transfer cycle process.Power transformer only has two states usually: run and stop transport.Stop transport and be divided into two states again: by forced-stopping machine (breaking down) and scheduled overhaul.Carry out state duration sampling,
A) original state is specified.Suppose that all transformers are all in running status, running status is 1, and shut down condition is 0, simultaneously number n of given emulation total year;
B) duration of each transformer current state is sampled, and the probability distribution of set condition duration (exponential distribution or lognormal distribution); Setting is T by the continuous working period of forced-stopping machine
f, the breakdown maintenance time is T
r, the time sequence status that Fig. 5 (a) is forced outage is sampled; The continuous working period of scheduled overhaul is T
sM, be generally definite value, as 1 year carries out a light maintenance, within 5 years or 10 years, carry out an overhaul, the scheduled maintenance time is T
sR, the time sequence status that Fig. 5 (b) is scheduled overhaul is sampled.Generate a certain transformer in interval equally distributed random number R
1, R
2and R
3, utilize inverse function, then the sample time of each state is respectively:
Wherein: setting T
fobeys index distribution, T
rand T
sRobeys logarithm normal distribution;
represent the inverse function of different distributions.
C) in studied time span, step b is repeated), namely obtain the time sequence status transfer process of a certain transformer in special time span and combine, as shown in Fig. 5 (c), until simulation time is greater than when n or coefficient of variation are less than the condition of convergence terminate emulation.A certain transformer combines is existed four kinds of states by after forced-stopping machine and scheduled overhaul, is respectively 11 (normally running), 10 (scheduled maintenances), 01 (breakdown maintenance) and 00 (time of carrying out breakdown maintenance was just in time in the time of original scheme of arrangement maintenance).Except 11 states, its excess-three kind state all belongs to " shutdown ".
Solve four state sequence Monte Carlo simulations, the probability distribution of downtime duration can be obtained.
Step (4), transformer Forecast of Economic Life model solution.Specifically:
According to step 1), calculate EUAC and predict the method for economic life and the annual total cost C of power transformer
arelevant, annual total cost is calculated as follows:
C
A(t)＝C
R(t)+C
I(t)+C
O(t)
In formula, C
rt () is the annual overhaul cost of t; C
it () is the annual outage cost of t; C
ot () is the annual operating cost of t.
Being calculated as follows of year each cost:
(1) annual overhaul cost C
r
C
R(t)＝(a×r
a+b)×λ(t)
In formula, C
rt () is the annual overhaul cost of t; A is for shutting down variable maintenance cost hourly; B is each fixing maintenance cost of interrupting; r
abe the mean down time of each fault of t, tried to achieve by the Monte Carlo Analogue Method of step (3); λ (t) is the failure rate of transformer t, is tried to achieve by the proportional hazards model of step (3).The cost unit related in formula is " unit ", and the value of a and b is determined according to transformer running environment and regional economy situation.
(2) annual outage cost C
i
Transformer stoppage in transit can have influence on power supply reliability, causes the loss of user.Can simplify and think that this part loss is for outage cost expense, need to select to set up the outage cost function relevant with downtime duration for this reason.Unit outage cost and downtime duration have with customer type relevant, determine according to the powered types in the geographical environment of power transformer place.For house class and commercial power supply, the unit outage cost expense under a certain downtime duration is as shown in table 3:
Unit outage cost expense under a certain downtime duration of table 3
Utilize cubic spline difference his-and-hers watches 3 data to carry out curve fitting, the unit outage cost function of different downtime duration can be obtained, as Fig. 6.
The unit outage cost function of different downtime duration, in conjunction with probability distribution stop time that Monte Carlo Analogue Method obtains, can predict the outage cost expense under specific load (kW) when obtaining each fault.Therefore annual outage cost formula is as follows:
In formula: C
it () is the outage cost of t, be the mean value of probability distribution; λ (t) is the failure rate of t; L
avfor the average load of transformer; SCDF
tit is the outage cost expense of t specific load (kW); K is downtime duration, by hour in units of, assuming that scope is [0,70]; p
ktto be t downtime duration the be probability of k hour, is tried to achieve by the Monte Carlo Analogue Method of step (3); C
tkfor the unit outage cost expense that downtime duration is k hour, with reference to Fig. 6.
(3) annual operating cost C
o
Annual operating cost is made up of two parts: energy loss cost and demand cost.Energy loss cost is relevant with the energy tax rate, because China does not set up special energy tax item, the tax category such as value added tax, the consumption tax all may with energy loss costs associated, weigh very difficult, therefore the present invention does not consider energy loss cost.Therefore, annual operating cost is exactly demand cost, as shown in the formula:
C
O(t)＝(P
nl+P
l+P
au)×D
c×12
In formula: C
ot () is the operating cost of t; P
nlfor no-load power loss (kW); P
lfor load loss (kW); P
aufor added losses (kW); D
cfor the demand electricity charge (unit/kW) monthly.
Meanwhile, the calculating of EUAC is also relevant with the present worth of power transformer, and computing method are as follows:
In formula, PV (t) is the transformer present worth in the t end of the year;
the accumulated depreciation expense to t from First Year, the formula in the same step of other variable (1).
The calculating of amortization charge needs the choice and operation considering depreciation method.The conventional time-based depreciation method is straight-line depreciation and accelerated depreciation.Straight-line depreciation and depreciation composite life, refer to a kind of method by the average calculating and distilling depreciation tenure of use of capital assets, discount rate is fixed; Accelerated depreciation method is divided into double decling balance method and sum of the years digits method.Wherein sum of the years digits method, the method that the year number mark referring to the state of tapering off distributes cost.Because power transformer is along with the increase of tenure of use, failure rate can rise, especially after operation the phase, and the value of transformer is substantially equal to residual value.Therefore, when transformer tenure of use more than 20 years time the present invention select sum of the years digits method computing depreciation expense, then adopted straightline method of depreciation before 20 years.
Application examples
For verifying the feasibility of the above-mentioned power transformer Forecast of Economic Life method based on lifetime data.Choose the life-cycle data analysis of 22 the 220kV transformers in somewhere.Transformer enlistment age span is [1,33]; Running environment is divided into manufacturing district and resident business building district, and code name is respectively 1 and 2; Have 8 manufacturers, code name is respectively 1 ~ 8; Because China's status monitoring development time is more late, the acquisition time unification of HI partial data is begin on Dec 31st, 2006.
1) active service transformer fault rate prediction.
According to PHM method for solving, from transformer life-cycle data, choose 196 groups of lifetime datas analyze, the statistical learning utilizing Statistica software to carry out distribution-free failure rate model calculates, and the regression coefficient vector β that can obtain in the failure rate PHM model of this area 220kV transformer is:
β＝(β
1,β
2,…,β
7)
T
＝(2.159,4.442,2.719,0.014,0.815,
0.214,-0.042)
T
As long as know a certain each covariant value of transformer, this transformer fault rate score just can be obtained.
Choose the transformer that current manufacturer's code name just is under arms 1, running environment is 2, electric pressure is 220kV, capacity is 180MVA, design service life is 35 years to analyze.This transformer put into operation on August 1st, 1992, up to now, had been on active service 22 years, and each covariant is Z=(0,0,0.1,22,2,1.5,1)
t, the failure rate expectation value after can being calculated by PHM.Because numerical analysis is afterwards all with " year " for unit, therefore this transformer each year failure rate expectation value of the 23rd year to the 35th year is all averaged, and concrete numerical value is as shown in table 4:
The failure rate expectation value that table 4 active service transformer is following annual
In table, the failure rate of prediction is in accumulative feature of risk, and show the increase along with the enlistment age, the possibility that fault occurs constantly strengthens.
2) calculating of active service transformer downtime duration probability distribution and outage cost function.
The power transformer current light maintenance cycle is 1 times/year, and the time between overhaul is 0.1 times/year, and average each scheduled maintenance time is 8 ~ 12 hours.Utilize sequential Monte Carlo to simulate the probability distribution that can obtain the downtime duration of each year of transformer, such as transformer runs the 23rd year, and λ (23)=0.010009578, the probability distribution of downtime duration as shown in Figure 7a.
Composition graphs 6, can obtain the outage cost expense of unit load, thus can the annual outage cost of calculating transformer further.
3) annual each pricing.
In annual overhaul pricing, r
acan obtain according to annual downtime duration probability distribution calculating mean value, a=965 (unit/hour) is determined in this application official holiday, and b=84696 (unit), then can obtain active service transformer annual overhaul cost according to table 4.
In year outage cost calculating, by the outage cost expense of known unit load above, the average load of this transformer is 25050kW, utilizes formula can obtain the annual outage cost of active service transformer.
In year operating cost calculating, according to transformer noload losses P
nlwith load loss P
lhistorical data, find change and little, therefore press 45.356kW and 208.435kW calculating respectively, ignore added losses P
au.Sale of electricity price in this area's is 0.538 yuan/kWh (non-peak-trough electricity), supposes that the every day average electricity consumption time is 8 hours, then monthly by 30 days, and demand electricity charge D
cbe 129.12 yuan/kW.Utilize formula can obtain the annual operating cost of active service transformer.
The above-mentioned cost of overhaul, outage cost and the operating cost calculated as shown in Figure 7b.
From Fig. 7 b, although the cost of overhaul increases along with enlistment age and increases, amplification is less, and compared with other costs, overall numerical value is less.Should operating cost in use-case, have employed constant, so operating cost is steady state value owing to calculating variable.Outage cost amplitude of variation is very large, reason is failure rate is the main factor affecting outage cost, because the future malfunction rate of prediction is in accumulative feature of risk, be equivalent to hypothesis from existing age, no longer carry out the activity of any inspection and maintenance, failure rate numerical value just presents quick ascendant trend, and therefore outage cost constantly rises.
4) EUAC calculating and change decision-making.
This transformer with about 1,500,000 yuan of purchases, supposed that residual value was zero originally, and when not considering interest rate, adopt with 20 years be boundary straightline method of depreciation and sum of the years digits method capitalizes, result of calculation as shown in Figure 7 c.
Transformer M=22 in existing age, supposes interest rate i=6%, can utilize the present worth in each prediction year of formulae discovery.According to history year operating cost and each annual prediction cost in future of above-mentioned gained, the EUAC curve in active service transformer following year can be obtained according to the formula in step (1), as shown in figure 7d.
From Fig. 7 d, the EUAC value curve minimum point of active service transformer appears at the 25th year, i.e. the optimal economic life-span N=25 of this transformer.This means, now age is this transformer in 22 years, supposes no longer to carry out any inspection and maintenance movable, and after 3 years, this transformer is retired comparatively economical.
Analyze known above, failure rate is the key factor affecting the economic life, if this transformer can improve O&M requirement in the operation in future, makes failure rate continue to keep low-level, then the optimal economic life-span can be made to continue to delay.On the contrary, if consider, these transformers of reason such as load growth have the demand of transformation, then can consider to reduce O&M requirement, retired comparatively economical after 3 years.
Claims (3)
1., based on a power transformer Forecast of Economic Life method for lifetime data, it is characterized in that,
First, minimum as retired foundation using transformer year equivalent cost, the economic life model of power transformer is proposed;
Then, classify and extract lifetime data, the proportional hazards model of selection distribution-free and Monte Carlo Analogue Method calculate the key parameter in the failure rate of power transformer and these two models of probability distribution of downtime duration;
Finally, integrated economics key element, proposes the computing method of the annual overhaul cost of transformer, outage cost, operating cost and present worth, realizes solving of Forecast of Economic Life model, obtain the optimal economic life-span of power transformer based on lifetime data.
2. the power transformer Forecast of Economic Life method based on lifetime data according to claim 1, it is characterized in that, it adopts following concrete steps:
Step 1), the foundation of the economic life model of power transformer;
According to cash flow diagram, past value in different time points or future value need conversion to reference time value, the present worth of certain moment amount of money is represented with P, F represents the final value of equivalence of a certain moment amount of money in the future, A represent fund on schedule single-candidate pay annuity, i.e. year equivalent cost EUAC, the conversion relation between them is as follows:
F＝P(1+i)
n，
In various above, i is discount rate; N is the conversion time limit;
During M+m, the total cost final value of transformer is:
In formula, M is the current enlistment age, and m is the m that will predict from the current enlistment age; FV
m+mthe cost final value of indication transformer M+m; C is transformer cost of capital; PV (M+m) is the present worth of transformer M+m after depreciation; C
aj () is the annual total cost in transformer jth year, wherein, the annual total cost now before M in age adopts historical data, and the data after existing age are predicted value;
EUAC is converted into by total cost final value:
In formula, EUAC
m+meUAC value during indication transformer M+m;
Step 2), the classification of life-cycle data and extraction;
Step 3), model parameter calculation;
From step 1), calculate EUAC and predict that the method for economic life is relevant with present worth with the annual total cost of power transformer, wherein, present worth is calculated by the depreciation method; Annual total cost needs the cost of overhaul and annual outage cost computation year, relates to the calculating of transformer reliability index and downtime duration probability distribution,
(1) foundation of failure rate forecast model
Use for reference widely used theory of survival analysis in medical science, the covariant set up the condition failure rate function on affecting survival condition: proportional hazards model, this model is regression model, and its mathematic(al) representation is as follows:
λ(t|Z)＝λ
0(t)c(β
TZ)，
In formula: λ
0t () is benchmark failure rate, relevant to the enlistment age; Z=(z
1, z
2..., z
p)
tfor covariant vector, covariant is the state variable of reflection equipment health condition, and p is covariant number, and T represents the transposition of vector; β=(β
1, β
2..., β
p)
tfor unknown regression coefficient vector; Contiguous function c is any nonnegative function, the simple exponential function of different forms, and namely the expression formula of proportional hazards model is as follows:
λ(t|Z)＝λ
0(t)exp(β
TZ)，
Logic inductive method is adopted to the lifetime data relevant with failure rate, condensed go out 7 covariants, be respectively outward appearance z
1, mechanical z
2, insulation z
3, enlistment age z
4, geographical running environment z
5, capacity-load ratio z
6with manufacturer z
7, above-mentioned 7 kinds of covariants are all relevant to equipment survival condition, are labeled as z
1(t) ~ z
7(t); If z
kt () had nothing to do with the time, k=1 ~ 7, be then expressed as z
k; For i-th transformer, its ratio failure rate function is as follows:
λ
i(t|Z
i(t))＝λ
0(t)exp(β
i TZ
i(t))
＝λ
0(t)exp(β
1z
i1(t)+β
2z
i2(t)+
…+β
7z
i7(t)),
In formula: time t and covariant vector Z are known quantity; λ
0t () and regression coefficient vector β are unknown quantity, work as λ
0when () is half parameter of distribution-free t, " partial likelihood function " method of employing solves regression coefficient β;
(2) Monte Carlo Analogue Method determines the probability distribution of break period
Adopt sequential Monte Carlo simulation to set up the probability distribution of downtime duration, utilization state duration sampling sets up virtual state transfer cycle process, when carrying out state duration sampling,
A) specify original state, suppose that all transformers are all in running status, running status is 1, and shut down condition is 0, simultaneously number n of given emulation total year;
B) duration of each transformer current state is sampled, and the probability distribution of set condition duration;
C) in studied time span, step b is repeated);
Step 4), transformer Forecast of Economic Life model solution
According to step 1), calculate EUAC and predict the method for economic life and the annual total cost C of power transformer
arelevant, annual total cost is calculated as follows:
C
A(t)＝C
R(t)+C
I(t)+C
O(t)，
In formula, C
rt () is the annual overhaul cost of t; C
it () is the annual outage cost of t; C
ot () is the annual operating cost of t;
Meanwhile, the calculating of EUAC is also relevant with the present worth of power transformer, and computing method are as follows:
In formula, PV (t) is the transformer present worth in the t end of the year,
be the accumulated depreciation expense to t from First Year, other variable is with the formula in step 1).
3. the power transformer Forecast of Economic Life method based on lifetime data according to claim 2, is characterized in that, step 4) in, being calculated as follows of annual each cost:
1) annual overhaul cost C
r
C
R(t)＝(a×r
a+b)×λ(t)，
In formula, C
rt () is the annual overhaul cost of t; A is for shutting down variable maintenance cost hourly; B is each fixing maintenance cost of interrupting; r
abe the mean down time of each fault of t, by step 3) in Monte Carlo Analogue Method try to achieve; λ (t) is the failure rate of transformer t, by step 3) in proportional hazards model try to achieve, the cost unit related in formula is unit, and the value of a and b is determined according to transformer running environment and regional economy situation;
2) annual outage cost C
i
Annual outage cost formula is as follows:
In formula: C
it () is the outage cost of t, be the mean value of probability distribution; λ (t) is the failure rate of t; L
avfor the average load of transformer; SCDF
tit is the outage cost expense of t specific load; K is downtime duration, by hour in units of, assuming that scope is 0-70; p
ktto be t downtime duration the be probability of k hour, by step 3) in Monte Carlo Analogue Method try to achieve; C
tkfor the unit outage cost expense that downtime duration is k hour;
3) annual operating cost C
o
Year operating cost as shown in the formula:
C
O(t)＝(P
nl+P
l+P
au)×D
c×12
In formula: C
ot () is the operating cost of t; P
nlfor no-load power loss, kW; P
lfor load loss, kW; P
aufor added losses, kW; D
cfor the demand electricity charge monthly, unit/kW.
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